Abstract
Nonlinear model predictive control (NMPC) is one of the few control methods that can handle multivariable nonlinear control systems with constraints. Gaussian processes (GPs) present a powerful tool to identify the required plant model and quantify the residual uncertainty of the plant-model mismatch. It is crucial to consider this uncertainty, since it may lead to worse control performance and constraint violations. In this paper we propose a new method to design a GP-based NMPC algorithm for finite horizon control problems. The method generates Monte Carlo samples of the GP offline for constraint tightening using back-offs. The tightened constraints then guarantee the satisfaction of chance constraints online. Advantages of our proposed approach over existing methods include fast online evaluation, consideration of closed-loop behaviour, and the possibility to alleviate conservativeness by considering both online learning and state dependency of the uncertainty. The algorithm is verified on a challenging semi-batch bioprocess case study.
Highlights
Model predictive control (MPC) describes an advanced control method that has found a wide range of applications in industry
Gaussian processes (GPs) nonlinear MPC (NMPC) 50, 60, 100: GP NMPC approach without learning and without taking into account state dependency for dataset sizes of 50, 60, and 100 points using the first type of dataset
GP NMPC learning 50: GP NMPC approach with learning and without state dependency for a dataset size of 50 points, which will be compared to the above case of 50 data points without learning
Summary
Model predictive control (MPC) describes an advanced control method that has found a wide range of applications in industry. The main advantage of MPC is its ability to deal with multivariate plants and process constraints explicitly (Maciejowski, 2002). NMPC is becoming progressively more popular due to the advancement of improved non-convex optimization algorithms (Biegler, 2010), in particular in chemical engineering (Biegler and Rawlings, 1991). The performance of MPC is greatly influenced by the accuracy of the plant model, which is one of the main reasons why MPC is not more widely used in industry (Lucia, 2014). NMPC algorithms exploit various types of models, commonly developed by first principles or based on process mechanisms (Nagy et al, 2007b). In Wu et al (2019a) the approach was extended updating the recurrent NNs online to further improve the effectiveness
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